A scalable pipeline for COVID-19: the case study of Germany, Czechia and Poland.

Abstract

Throughout the coronavirus disease 2019 (COVID-19) pandemic, decision makers have relied on forecasting models to determine and implement non-pharmaceutical interventions (NPI). In building the forecasting models, continuously updated datasets from various stakeholders including developers, analysts, and testers are required to provide precise predictions. Here we report the design of a scalable pipeline which serves as a data synchronization to support inter-country top-down spatiotemporal observations and forecasting models of COVID-19, named the where2test, for Germany, Czechia and Poland. We have built an operational data store (ODS) using PostgreSQL to continuously consolidate datasets from multiple data sources, perform collaborative work, facilitate high performance data analysis, and trace changes. The ODS has been built not only to store the COVID-19 data from Germany, Czechia, and Poland but also other areas. Employing the dimensional fact model, a schema of metadata is capable of synchronizing the various structures of data from those regions, and is scalable to the entire world. Next, the ODS is populated using batch Extract, Transfer, and Load (ETL) jobs. The SQL queries are subsequently created to reduce the need for pre-processing data for users. The data can then support not only forecasting using a version-controlled Arima-Holt model and other analyses to support decision making, but also risk calculator and optimisation apps [1, 2]. The data synchronization runs at a daily interval, which is displayed at https://www.where2test.de.

1. Introduction

realise the data surveillance and outbreak response management, which have been implemented in fighting other In building forecasting models of COVID-19, many re- endemic diseases [ 4, 5, 6, 7 ]. searchers employ the training datasets provided by each To date, the data management have been applied in country’s representative institutions, e.g., Robert Koch controlling the outbreak of COVID-19 [8, 9, 10, 11, 12, Institute in Germany. The publicly accessible COVID- 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Most of them pro19 data provided in raw textual format, such as CSV, vide maps and the prevalent data in the following reJSON, and XML are downloaded and analysed by the gional level: (i) National level, e.g., COVID-19 data of researchers employing either statistical or machine learn- World wide [ 10 ], Europe [ 11, 12, 13 ], and Latin Amering approaches. However, the data are unwell struc- ica [ 14 ]; (ii) State and county levels, e.g., the COVID-19 tured and require heavy pre-processing as well as in- data warehouse for Italy [ 15 ], COVID-19 dashboard for gestion activities for further analysis. This method is UK [ 17 ], the COVID-19 dashboard for Maryland [18], inherently ineficient due to identical and manual paral- and for Germany [19].; (iii) County level, e.g., Dresden, lel pre-processing of the RKI data (using e.g. python or Germany [20]. More completed version is provided by R scripts) performed by each researcher. This reduces the John Hopkins University [21], which serves the dashthe eficiency of each and everyone’s work as all have to board and the prevalent data for each regional level in spend hours and days in pre-processing data before com- the USA as well as for most of countries around the ing to modeling and forecasting. Advanced computing world. Likewise, the similar method in the presence infrastructures and novel software pipelines are crucial of semi-automatic validation strategy was conducted to tools to synchronize the data structures which originate check the data quality of daily updated numbers with from various sources and to extremely reduce heavy pre- governmental/oficial data sources [ 22]. However, most processing [ 3 ]. They serve as essential prerequisites to of dashboards and data warehouses have not provided the features to let the users perform an inter-country Proc. of the First International Workshop on Data Ecosystems (DEco’22), top-down spatiotemporal observation, i.e., observing the September 5, 2022, Sydney, Australia inter-country prevalence and simultaneously being able * Corresponding author to observe to the microscopic level (nation → state → ($J. Mw..aCbadluasbsraelsaem)@hzdr.de (W. Abdussalam); [e-mail] county → municipality). The features could provide in© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License sights, for example, to study COVID-19 border dynamCPWrEooUrckReshdoinpgs IhStpN:/c1e6u1r3-w-0s.o7r3g ACttEribUutRion W4.0oInrtekrnsahtioonpal (PCCroBYce4.0e).dings (CEUR-WS.org) ics which have been so far attracted considerable attentions [23, 24, 25, 26]. Moreover, they are lack of forecasting features, which play a key role in predicting the future prevalence as well as determining non pharmaceutical interventions (NPI). A tremendous number of forecasting models, e.g., agent-base [27], machine learning [ 28, 29 ], combination model [ 30, 31 ], compartment model [ 32, 33, 34, 35, 36 ], time series [ 37, 38, 39, 40, 41, 42, 43 ] have employed government datasets to provide essential inputs for public decisions. However, most of datasets that were used in those studies are limited to the specific time window which are likely to produce diferent results when the datasets are updated. Establishing a system of daily-updated-datasets assisted forecasts, therefore, is an alternative to improve their consistency and precision.

In this paper, we address the aforementioned issues by proposing the design of a scalable pipeline which allow us to perform the top-down spatiotemporal observation among Germany, Czechia, and Poland as well as to perform daily forecasts. The method of the pipeline which consists of extraction of various data sources and the ODS is described in subsec 2.1. More specifically, we will describe the dimensional fact database model and a daily migration process which underline the data synchronization between various data sources and our Figure 1: (a) A workflow of data pipeline Hospitals, retiredatabase server. We employ the dimensional fact model ment houses, and schools of Germany, Czechia and Poland due to more flexibility and versatility in building spa- update the data of COVID-19 cases, vaccines and tests to the tiotemporal aggregation functions than the nanocubes representative government institutions. A daily automatic ETL model [44, 45]. Next, in subsec 2.2 we will describe the step is performed to synchronize the data sources and central time-series forecasting models which are supported by database of CASUS. A daily and weekly automatic forecast the presence of the ODS. Furthermore, the automatic employing, e.g. Arima-Holt model, is applied to provide rapid system of daily forecasts owing to the presence of the predictions. The predictions and the actual data are shown pipeline will be laid out in this sub section. In Sec. 3, we in the where2test website; (b) The scalable dimensional fact will describe facilities that have been established due to wmhoidleelr.eDgiaotnavtyalpueessaannddtdimateapvearliuoed ttyyppeess rreepprreesseenntt smpaetaiasularnesd, the presence of the ODS. In order to demonstrate the temporal dimensions, respectively. inter-country top-down spatiotemporal observations, an analysis will begin from the macroscopic scale in which the study of the virus spread across the national borders is described in subsec 3.1. Herein we consider the border 2. Methods among Germany, Czechia and Poland as a study case.

In subsec 3.2, we explore more microscopic level by ap- 2.1. Data Pipeline plying a daily-updated-datasets assisted forecast for the Fig. 1a shows a workflow of the data pipeline. The hosprevalence in the state of Saxony, Germany. Last but pitals, retirement houses and schools register the daily not least, in subsec 3.3, most microscopic level that we number of the COVID-19 cases and vaccines to the repwill demonstrate is a superspreading event at a slaugh- resentative government. In order to consolidate these ter house in Gütersloh, Lower Saxony, Germany. As the data, the relational database is built based on dimenCOVID-19 situation begins to enter an endemic phase, sional fact model [46]. Having established the relational a study of superspreading event will provide essential database, the daily automatic extract, transfer and load information to trace the COVID-19 transmission after a (ETL) step is performed to migrate and integrate the data mass event. sources to the PostgreSQL database of CASUS HZDR (see Suplementary materials 7.1). Next, we create SQL inquiries-based views to be analysed by our researchers using the forecast and machine learning methods. The tested and completed analysis methods are set in the master stage and the other tested methods are set in the develop stage. Only the forecasting method in the master 2.2. Forecasts stage is integrated in the automatic pipeline.

The dimensional fact model is shown in Fig. 1b. The We employ auto regression integrated moving average model consists of three main concepts: (i) Facts, that (ARIMA) and Holt’s linear trend models to forecast the refer to a subject of study (e.g., the study of infected, infected, test, and hospitalised data of COVID-19 for dead, recovered, hospitalised, test and vaccinated cases Saxony (Germany), Czechia, and Poland. The ARIMA due to COVID-19); (ii) Measures, that refer to the quan- model has been successfully employed in predicting other titative data of the concept (i). The measured data are endemic diseases [ 47, 48, 49, 50 ]. The model features stored in the table of datavalues. The tables of datavalues suitable prediction based on time analysis series which contain the number of infected, dead, recovered, hospi- is capable of providing short horizon forecast for most talised, test, and vaccinated cases due to COVID-19 in COVID-19 cases around the world [38, 39, 40, 41, 42, 43]. a given time and place. To date, the schema consists of To make the model consistent and avoid overfitting, the three datavalues, i.e., datavalues of Germany, Czechia order parameter of the ARIMA model is fixed instead of and Poland; (iii) Dimensions, that refer to temporal and using the auto ARIMA model. The ARIMA is improved spatial attributes. As the measured data are provided in a by employing the Holt’s linear trend model [ 51 ]. The given time and place, the table of time period types and Holt’s model uses the exponential smoothing method to regions is necessary. The former stores the type of time compute the weighted average of the past observation period which consists of day and week data type; and the data [ 52 ]. The forecasts from the Holt’s linear model have latter stores the necessary information of regions which a trend, so the damped parameter is turned on to avoid consist of the name, abbreviation, ID of regions, ID of this trend [ 53, 54, 52 ]. A self-defined mix function is used region type, geometry and population. The table of re- to compute the probability parameter m to combine the gions depends on the table of region types. The regions forecasts from two models and minimize the error. The are categorised based on their sizes. The order of as- Box-Cox transformation is used to normalize the input cending sizes starts from municipality, county, state and data [ 55, 52 ]. nation. For Germany, the order of region type starts from Our model provides a weekly forecast at first. In order Gemeinde, Kreise and Bundesland. Similar to Germany, to improve the daily variation and provide more realPoland consist of Gmina, Powiat, and Wojewodztwo. Dif- time forecasts, we have built a daily forecast model. As ferent from Germany and Poland, Czechia consist of 4 the daily data have a clear weekly variation, the sealevel, Obec, Orp, Okres and Kraj. The spatial and tempo- sonal parameters are added to the model; and seasonal ral attributes are connected by means of hierarchies to ARIMA (SARIMA) and Holt-Winters’ seasonal model are represent a -to-one relationship between them. The table employed for the daily forecasts [ 56, 51, 57 ]. Similar to of mapping_types contains the hierarchical type of the the ARIMA model, the seasonal ARIMA model uses the spatial attributes, e.g., for Germany (Gemeinde to Kreise, ifxed order and seasonal parameters. After comparing Kreise to Bundesland), for Czechia (Obec to Orp, Orp to the errors from multiple methods, the additive method is Okres and Okres to Kraj), and Poland (Gmina to Powiat selected for the Holt-Winters’ seasonal model. The mix and Powiat to Wojewodztwo). Next, a many-to-one re- function is also used for the daily forecasts to combine lationship between those spatial hierarchies are stored the forecasts from two models and improve the forecastin the table of mapping_regions. Moreover, the table of ing accuracy. For study cases of (S)Arima-Holt model, timeperiod_types consists of the hierarchical type of the in Sec. 3.2, we will provide the number of infections for temporal attributes. Saxony, Germany. In addition to (S)ARIMA-Holt model,

Aggregation functions are applicable on the measures we employ outlier detection to identify and quantify Sualong the temporal and spatial dimensions. For the for- perspreading events. As suggested in [ 35 ], we identify mer dimension, the weekly data are cumulative 7–day and quantify superspreading events by using time sedata. For example, a 7–day case reported on 13.03.2022 is ries analysis based outlier detection methods. The rate an accumulation of the daily case for 07-13.03.2022. More- of newly infected is modeled by an appropriate model, over, for the latter dimension, county data are cumulative- which could be something as simple as a rolling average municipality data. Not only accumulating the data from to more elaborate ones as SIR-based models. The residues the municipality to a county level, in the presence of of the reported cases is used to identify outliers. At the mapping regions table, it is possible to accumulate the same time, the residues can be used to quantify the size data from the county to the state level as well as the state of a superspreading event. to the nation level. This allows us to scale the pipeline to other areas provided that the data of municipality are 3. Results available from the sources.

The presence of the pipeline has allowed us to provide following facilities: (i) The released data hub for dead and infected cases of all counties and states in Germany [58], which allows a collaboration between CASUS research stafs and other external collaborators. The post-processing data serve as the clean data of daily infected and dead cases for county and state levels. In addition, we have also pre-processed the vaccination and hospitalization data for the county and municipal levels; (ii) The daily updated value of background risk for optimisation [ 1 ] and risk calculator apps [ 2 ], which defines the chance of an average person who lives in the focal area, and carries out daily activities, will be infected over a one week period; (iii) Blog posts which update current COVID-19 situations in Germany. An interesting example of the posts would be the relation between the vaccination rate and the 7-day incidence in all states of Germany [59]; (iv) Forecast- and model-based analysis. We explore the study cases mentioned in Sec. 1, and begin by investigating of the virus spread across the national borders of Germany, Czechia, and Poland. wise correlations for each region considering the regions in the radius of 100 kilometers, (i) within the same coun3.1. Analysis of the virus spread across try, (ii) outside this country. The diference of these valthe national borders ues can be seen in Fig. 2. The bigger diference represents regions where the incidence correlates much better than COVID-19 spread among people. Therefore, human mo- the regions within the same country, indicating a strong bility is one of the most important factors defining the national border efect on the virus spread. trend of spatiotemporal spreading of the virus. Under- In the next step [63], we quantified the mitigation efect standing human mobility allows us to predict the spa- of the national border in more detail. We picked the state tiotemporal character of spread, evaluate the government of Saxony in Germany and the neighboring regions in steps restrictions, and provide efective non-pharmaceutical Czechia. For both countries, we collected and integrated interventions. Primarily due to the heterogeneity of the the incidence data on the level of single municipalities. sources and the interest scope of the particular research For each municipality, we constructed a local regression groups and communities, most of the COVID-19 research model which estimated the efect of three parameters, (i) stays within the boundaries of one country. While most border presence, (ii) municipality size, and (iii) temporal human mobility happens in the extent of one country or distance from other municipalities, on the spread of the region, notably in Europe, the national border’s mitigat- virus. Based on this model, we identified very smalling efect is generally diminishing. To study the impact scale areas susceptible to a more intensive inter-national of the national border, several research papers [60, 61] ap- spread of the COVID-19. plied various methodologies of geostatistics and geospa- The top-down approach we selected for the study on tial modeling. More thorough quantification of the efect the national border efect is possible thanks to the scalaof border presence and international mobility on the epi- bility of the implemented dimensional-fact model. This demy requires a data storage integrating heterogeneous principle allows the ODS to comprise various adminisdatasets across more countries. trative levels and combine various relevant topics within

The presented ODS infrastructure ofers a possibility the perspective of spacetime. to study the spatiotemporal character of the virus spread on more levels, considering the efect of the national border. First, for our case study comprising the coun- 3.2. Weekly and daily forecast of tries of Germany, Poland, and Czechia, we explored the Arima-Holt and Sarima-Holt correlation of new cases in the region, the distance and For the case study, we provide a short-time forecast of 7the border presence. We observed that the neighbour day incidence up to 4 horizons performed on 13-04-2022 regions tend to have similar incidence values in the ab- using Arima-Holt model for Saxony, Germany. We used sence of barrier in the form of a national border among a training dataset of 13-04-2022 version which consists of them. This step followed the research of McMahon et al. the historical weekly data of Saxony and its counties from [62], which showed a strong spatial autocorrelation of 01-03-2020 to 10-04-2022. The weekly data are automatedincidence values in the USA. daily-updated data which are aggregated on Sunday (see Further, we calculated the average time-lagged paira diferent day, a deviation from the actual data for the following 4 horizons is likely to occur. Additional realisations of Arima-Holt forecast in Saxony and its counties, therefore, were performed to improve statistics. The realisations were performed every Wednesday from 05-012022 to 18-05-2022 in which the version-control dataset were employed as training and test datasets. An example would be a realisation of the Forecast on 05-01-2022. We Figure 3: 7-day incidence of infected cases Jan - 8 May 2022 used the weekly data version of 05-01-2022 as its training for Saxony, Germany. The black dots denote the historical dataset and the weekly data version of the following 1st, data, the blue line (—) denotes a line guidance for the historical 2nd, 3rd and 4th week as its test datasets. For each region, data, and the green (—), orange (—), and red line (—) denotes we then recorded a deviation of the forecast result from tgohrneey1r0ea-sr0ue4al-t2so0hf2of2wo,rs1e1tch-a0es4tl-ou2w0si2enr2g,aatnhndeduA1p3rpi-me0r4al--i2mH0oi2tl2st,omrfeosthdpeeelcftpoireverecfloayrs.mtTfheoder tpheerchenisttaogreicearlrodrat(MaAanPdE)q. uAasnsthifieodwint iansFmige. a4n,thabeswoleuetkely 13-04-2022. Arima-Holt provides relatively low MAPE for the first and second horizon. For the third and fourth horizon, however, the range of MAPE tends to be wider than the ifrst and second.

Sec. 2.1). Although we update the data daily, for the Therefore, we performed the Sarima-Holt model to case of Germany, the current and previous-day data are improve the performance of forecast for the third and unavailable. In addition, the previous third day data are fourth horizon. Owing to daily-updated data, the versionstill to be updated from the source. When the forecast was control of daily data is employed as the seasonal paperformed on Sunday 10-04-2022, the number of infection rameters. In addition to the daily data, the Sarima-Holt on that day was less than the number of the same day forecast was performed using the same version-control for the following-day version. As a result, this produces weekly data employed to the Arima-Holt model. For the inaccurate forecast (see Fig. 3). As the day elapsed, more daily data, we removed the current and two previouscases were automatically added and aggregated to the last day data due to zero values for current and yesterday Sunday data. Consequently, the performed forecast on data, and inconsistent data for the previous third day. We 13-04-2022 provides higher exponent than the one with then compared its performance in the presence and the the dataset version of 10 and 11-04-2022. Moreover, the absence of the Box-Cox transformation (BCT) used to dataset of Wednesday consists of relatively-stable version. normalize the input data. As shown in Fig. 4, the SarimaTherefore, the forecast is performed every Wednesday Holt model in the absence of the BCT provides lower due to the consistency of data source for the last Sunday. MAPE than either the Arima-Holt or the Sarima-Holt in the presence of the BCT for not only the first and second horizons, but also the third and four horizons.

3.3. Superspreading events

conditions combined with relatively close physical dis- The Sarima-Holt model is trained by the daily data, and tance between workers were likely the main reason for the variation of the data could make the model more eficient aerosol transmission [ 66]. We take this event as sensitive to the infection change compared to the Arimaan example to show the result of a Z-score based outlier Holt model trained by the weekly data. However, the detection method (Fig. 5). BCT reduces the variation of the daily data, and consequently the daily forecasts perform worse than in the absence of the BCT.

5. Conclusion

Our work has demonstrated the utility of the data pipeline

for top-down spatiotemporal analysis. We have first shown the macroscopic analysis, in which the investigation of the virus spread across the national border is presented. At more microscopic level, we have demonFigure 5: The oficial reported COVID-19 daily incidence strated data-driven approach due to the presence of the spperre1a0d0i.n0g00evinehnatbiintaantms einatthperodciesstsriicntgopflGanütteirnslJouhn.eA2s0u2p0eirs- pipeline which is applied to the prevalence of the county successfully identified by an outlier detection method based region. The daily-updated data has improved the precion the Z-score (the black dot). sion of the model for longer horizon. This data-driven epidemic models provide more realistic forecast results than either the parsimonious [ 34 ] or more number of parameters with agent-based method [27] due to the us4. Discussions age of daily-updated data. This may contribute to public health policy making, including contributing to public Our analysis, implementing the pipeline in the presence health forecasting teams. Last but not least, exploring of dimensional fact model has allowed us to daily mi- to lower level of region, we have demonstrated that the grate the data eficiently due to the functions of spa- outlier model is applicable to capture the superspreading tiotemporal aggregation. To provide the weekly data of event which occurred in 2020. These have shown that counties, states, and nations, we only migrate the data of our work is capable of performing top-down analysis as daily municipalities/counties (depends on the data avail- well as rapid and precise forecasts due to the presence of ability of each nation) to the database server which are the pipeline. then aggregated to the higher spatiotemporal level. This model provides more advantages than the nanocubes 6. Data sources model [44, 45]. For the nanocubes model, each spatial (municipality, county, state and nation) and temporal • COVID-19 data for Germany, Czechia and Poland. (daily and weekly) data are required to be migrated to the database server. Consequently, this leads to a longer – Robert Koch Institute migration process than the one performed using the di- – Czech Ministry of Health mensional fact model. Moreover, its spatiotemporal map- – Polish Ministry of Health ping enables us to perform an eficient table join among – Age-based hospitalisation of state level for national data which is confirmed by the application on Germany (https://github.com/KITmetricsl the Subsec. 3.1. ab/hospitalization-nowcast-hub/blob/ma

The presence of daily-updated data due to the presence in/data-truth/COVID-19/). of the pipeline has allowed us to develop the Sarima-Holt – Age-based and type-based doses of vaccine model. The model shows more robust prediction for for county level (https://github.com/rober longer horizon than the Arima-Holt one. More specifi- t-koch-institut/COVID-19-Impfungen_i cally, the Sarima-Holt in the absence of the BCT outper- n_Deutschland/blob/master/Aktuell_De forms the Arima-Holt model for the third and fourth hori- utschland_Landkreise_COVID-19-Impfu zon. This performance is due to the seasonal-parameter ngen.csv). contribution to the model. As a result, the forecast tends – COVID-19 infected, recovered, hospitalised to better predict for the third and fourth horizon. In con- and dead cases of Dresden (http://daten.dr tradiction, the Sarima-Holt in the presence of the BCT esden.de/duva2ckan/f iles/de-sn-dresden provides lower performance than the absence one due to -corona_-_covid-19_-_fallzahlen_md1_d less variation of the training data after BCT (see Fig. 7). resden_2020ff/content). – COVID-19 infected, dead, and test cases of Czechia for Municipality level (https: //onemocneni-aktualne.mzcr.cz/api/v2/c ovid-19/). – Age-based and gender-based infected and dead cases for county level of Germany (https://experience.arcgis.com/experience /478220a4c454480e823b17327b2bf1d4). – COVID-19 cases for municipality level of

Saxony, Germany (https://www.coronavi rus.sachsen.de/corona-statistics/rest/inf ectionOverview.jsp). – COVID-19 cases for county level of Saxony,

Germany (https://media.githubuserconten t.com/media/robert-koch-institut/SARS -CoV-2_Infektionen_in_Deutschland/ma ster/Aktuell_Deutschland_SarsCov2_Infe ktionen.csv) – COVID-19 infected, dead, and test cases for county level of Poland (https://wojewo dztwa-rcb-gis.hub.arcgis.com/pages/dane -do-pobrania). – COVID-19 vaccine for county level of Poland (https://www.gov.pl/web/szczepimysie/ra port-szczepien-przeciwko-covid-19). – COVID-19 types in Sachsen (https://www.

coronavirus.sachsen.de/infektionsfaelle-i n-sachsen-4151.html). • Dictionaries of regions.

– Administrative areas in Germany (https: //gdz.bkg.bund.de/index.php/default/digi tale-geodaten/verwaltungsgebiete.html). – Administrative areas in Poland (https://gi s-support.pl/baza-wiedzy-2/dane-do-pob rania/granice-administracyjne/) – Administrative areas in Czechia (https://ge oportal.cuzk.cz/(S(1nhx02lray0vkrhce1y2 d53d))/Default.aspx?mode=TextMeta&te xt=dSady_RUIAN&side=dSady_RUIAN) – Population numbers in Czech municipalities (https://www.czso.cz/csu/czso/pocet -obyvatel-v-obcich-k-112021) – Postal codes in Germany (https://www.ge onames.org/postal-codes/postleitzahle n-deutschland.html) – Population numbers in Poland (https://st at.gov.pl/obszary-tematyczne/ludnosc/lu dnosc/ludnosc-stan-i-struktura-ludnosc i-oraz-ruch-naturalny-w-przekroju-teryt orialnym-stan-w-dniu-30-06-2021,6,30.h tml)

7.1. Data workflow

We use https://www.talend.com/products/talend-openstudio/ to perform data migration. The migration between the data sources and the PostgreSQL database of CASUS HZDR has been performed as follows:

Poland, we add ’DE’, ’CZ’, ’PL’, respectively, followed by the intrinsic ID. For the table of regions, the primary key of region_types serves as its foreign key. The intrinsic IDs are categorised based on the ID of region types. A specific example would be Dresden, whose the intrinsic ID 14162. After cleaning processes, the intrinsic ID will be DE 14162 and categorised to the state level of Kreise.

Having migrated the data to the aforementioned tables, the table of mapping_regions is occupied by the spatial-relation data. It contains the foreign key of the mapping type ID. An example would be a county Dresden. Dresden are mapped onto the state of Saxony and categorized to the mapping type Kreis_To_Bundesland. Next, the table of datavalues for nations is occupied by the data input. The datavalues table consists of three foreign keys which originate from the tables of timeperiod_types, regions, datavalues_types. In the presence of these foreign keys, a data merging process is feasible, which is described on the following item. 4. Data merging In addition to the aforementioned three-foreign keys, date is set as the fourth attribute which allow us to perform data merging through inner join of tables. The inner join is employed to cleanly merge and avoid duplicated data on the table of datavalues. For instance, daily infected data of the lowest-level region for period of date are migrated to the table of datavalues_germany. When the data sources are updated, they sometimes update the cases of the elapsed date. Inner join method allows us to automatically update the value of the elapsed date by the latest value. Moreover, when the new data with the latest date are present from the source, it allows automatic addition of the data to the table. 5. Data aggregation The presence of daily data of the lowest regions allow us to perform both time and spatial aggregations. Using functions, the time aggregation from daily to weekly period is feasible. Moreover, as mentioned on the Sec. 2, the spatial aggregation from the low to the high region level is allowable in the presence of the mapping_regions table.

7.2. Additional forecasting results

Acknowledgments

This work was partially funded by the Center of Advanced Systems Understanding (CASUS), which is financed by Germany’s Federal Ministry of Education and

Research (BMBF) and by the Saxon Ministry for Science,

Culture and Tourism (SMWK) with tax funds on the basis of the budget approved by the Saxon State Parliament. We thank to Jens Steiner for providing us virtual server of HZDR.

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